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We describe the next set of experiments proposed in the U.S. Heavy
Ion Fusion Virtual National Laboratory, the so-called Integrated Beam
Experiment (IBX). The purpose of IBX is to investigate in an integrated
manner the processes and manipulations necessary for a heavy ion fusion
induction accelerator. The IBX experiment will demonstrate injection,
acceleration, compression, bending, and final focus of a heavy ion beam
at significant line charge density. Preliminary conceptual designs are
presented and issues and trade-offs are discussed. Plans are also
described for the step after IBX, the Integrated Research Experiment
(IRE), which will carry out significant target experiments.

We consider beams that are described by a four-dimensional
(4D) transverse distribution f (x, y,
x′, y′), where x′ ≡
px /pz
and z is the axial coordinate. A two-slit scanner is commonly
employed to measure, over a sequence of shots, a two-dimensional (2D)
projection of such a beam's phase space, for example,
f (x, x′). Another scanner might yield
f (y, y′) or, using crossed slits,
f (x, y). A small set of such 2D scans does
not uniquely specify f (x, y, x′,
y′). We have developed “tomographic” techniques
to synthesize a “reasonable” set of particles in a 4D phase
space having 2D densities consistent with the experimental data. We
briefly summarize one method and describe progress in validating
it, using simulations of the High Current Experiment at Lawrence
Berkeley National Laboratory.

The Heavy Ion Fusion Virtual National Laboratory High Current
Experiment (HCX) is exploring transport issues such as dynamic
aperture, effects of quadrupole rotation, and the effects on
the beam of nonideal distribution function, mismatch, and
electrons, using one driver-scale 0.2 μC/m, 2–10
μs coasting K+ beam. Two- and three-dimensional
simulations are being done, using the particle-in-cell code
WARP to study these phenomena. We present results which predict
that the dynamic aperture in the electrostatic focusing transport
section will be set by particle loss.

This article presents analytical and simulation studies of
intense heavy ion beam propagation, including the injection,
acceleration, transport and compression phases, and beam transport
and focusing in background plasma in the target chamber. Analytical
theory and simulations that support the High Current Experiment
(HCX), the Neutralized Transport Experiment (NTX), and the advanced
injector development program, are being used to provide a basic
understanding of the nonlinear beam dynamics and collective
processes, and to develop design concepts for the next-step
Integrated Beam Experiment (IBX), an Integrated Research Experiment
(IRE), and a heavy ion fusion driver. Three-dimensional nonlinear
perturbative simulations have been applied to collective
instabilities driven by beam temperature anisotropy, and to
two-stream interactions between the beam ions and any unwanted
background electrons; three-dimensional particle-in-cell
simulations of the 2-MV electrostatic quadrupole (ESQ) injector
have clarified the influence of pulse rise time; analytical
studies and simulations of the drift compression process have
been carried out; syntheses of a four-dimensional particle
distribution function from phase-space projections have been
developed; and studies of the generation and trapping of stray
electrons in the beam self-fields have been performed.
Particle-in-cell simulations, involving preformed plasma, are
being used to study the influence of charge and current
neutralization on the focusing of the ion beam in NTX and in
a fusion chamber.

For the intense beams in heavy ion fusion accelerators, details
of the beam distribution as it emerges from the source region
can determine the beam behavior well downstream. This occurs
because collective space-charge modes excited as the beam is
born remain undamped for many focusing periods. Traditional
studies of the source region in particle beam systems have
emphasized the behavior of averaged beam characteristics, such
as total current, rms beam size, or emittance, rather than the
details of the full beam distribution function that are necessary
to predict the excitation of the collective modes. Simulations
of the beam in the source region and comparisons to experimental
measurements at Lawrence Berkeley National Laboratory and the
University of Maryland are presented to illustrate some of the
complexity in beam characteristics that has been uncovered as
increased attention has been devoted to developing a detailed
understanding of the source region. Also discussed are methods
of using the simulations to infer characteristics of the beam
distribution that can be difficult to measure directly.

Significant experimental and theoretical progress has been
made in the U.S. heavy ion fusion program on high-current sources,
transport, and focusing. Currents over 200 mA have been transported
through a matching section and 10 half-lattice periods with
electric quadrupoles. An experiment shows control of high-beam
current with an aperture, while avoiding secondary electrons.
New theory and simulations of the neutralization of intense
beam space charge with plasma in various focusing chamber
configurations predict that near-emittance-limited beam focal
spot sizes can be obtained even with beam perveance (ratio of
beam space potential to ion energy) >10× higher than
in earlier HIF focusing experiments. Progress in a new focusing
experiment with plasma neutralization up to 10−3
perveance, and designs for a next-step experiment to study beam
brightness evolution from source to target are described.

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